Hi David,
Well here's the deal with Expedia and the other travel sites. If you booked through the Expedia site and did a prepaid reservation for 6 nights you actually paid Expedia not the hotel. In turn Expedia pays the hotel on one of their company cards a rate less than what you paid Expedia - this is why 1. you will not get a receipt from the hotel - it isn't your receipt it is Expedia's receipt (your receipt is technically your credit card statement showing the billing from Expedia and/or the emailed confirmation from Expedia that shows how much your credit card was charged and where you went, how long your stay was booked for, etc.) 2. The hotel cannot issue a refund for unused nights because they are basically dealing with Expedia not you. I don't think you will win this one by submitting a claim to your credit card company because the sites like Expedia specifically state that you cannot cancel or get a refund for unused nights.
If you book your overnight accomodations with the hotel directly then you have more of an opportunity to check out early if your business finishes ahead of schedule and you will be able to get a receipt from the hotel because you dealt directly with them.